Existence results for diffusion–convection equations of nonlinear unilateral problems defined in Orlicz–Sobolev spaces

摘要

We prove the existence result of unilateral problems associated to strongly nonlinear elliptic equations whose model, including the diffusion–convection equation, is ? ΔMu ?div(|u|p?1) = f. We study exactly the following general case Au ?div(Φ(x,u)) = f, where A is a Leray–Lions operator having a growth not necessarily of polynomial type, the lower order term Φ : Ω × ? → ?N is a Carathéodory function, for a.e. x ∈ Ω and for all s ∈ ?, satisfying only a growth condition and the right-hand side f belongs to L1(Ω).